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第 0 章 前言
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第 0 章 前言
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0.1 关于本书
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0.2 如何使用本书
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0.3 小结
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第 1 章 初识算法
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第 1 章 初识算法
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1.1 算法无处不在
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1.2 算法是什么
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1.3 小结
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第 2 章 复杂度分析
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第 2 章 复杂度分析
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2.1 算法效率评估
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2.2 迭代与递归
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2.3 时间复杂度
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2.4 空间复杂度
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2.5 小结
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第 3 章 数据结构
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第 3 章 数据结构
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3.1 数据结构分类
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第 6 章 哈希表
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7.1 二叉树
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7.2 二叉树遍历
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7.3 二叉树数组表示
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7.4 二叉搜索树
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7.5 AVL 树 *
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7.6 小结
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第 8 章 堆
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8.1 堆
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8.2 建堆操作
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8.3 Top-K 问题
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8.4 小结
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第 9 章 图
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第 9 章 图
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9.1 图
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9.2 图基础操作
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9.3 图的遍历
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9.4 小结
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< div class = "md-nav__link md-nav__container" >
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第 10 章 搜索
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第 10 章 搜索
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.1 二分查找
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_insertion/" class = "md-nav__link" >
< span class = "md-ellipsis" >
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10.2 二分查找插入点
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< li class = "md-nav__item" >
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10.3 二分查找边界
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< / span >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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10.4 哈希优化策略
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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10.5 重识搜索算法
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.6 小结
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< / span >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z" / > < / svg >
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第 11 章 排序
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第 11 章 排序
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< / label >
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11.1 排序算法
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11.2 选择排序
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< li class = "md-nav__item" >
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11.3 冒泡排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.4 插入排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.5 快速排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.6 归并排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
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11.7 堆排序
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< / span >
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
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11.8 桶排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
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11.9 计数排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
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11.10 基数排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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11.11 小结
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< / span >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z" / > < / svg >
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第 12 章 分治
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第 12 章 分治
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< / label >
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12.1 分治算法
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< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/binary_search_recur/" class = "md-nav__link" >
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12.2 分治搜索策略
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< / span >
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12.3 构建树问题
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< li class = "md-nav__item" >
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12.4 汉诺塔问题
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< a href = "../../chapter_divide_and_conquer/summary/" class = "md-nav__link" >
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12.5 小结
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第 13 章 回溯
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第 13 章 回溯
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13.1 回溯算法
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13.2 全排列问题
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13.3 子集和问题
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13.4 N 皇后问题
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13.4 N 皇后问题
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目录
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1. 逐行放置策略
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3. 代码实现
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13.5 小结
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第 14 章 动态规划
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14.1 初探动态规划
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14.2 DP 问题特性
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14.3 DP 解题思路
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14.4 0-1 背包问题
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14.5 完全背包问题
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14.6 编辑距离问题
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14.7 小结
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第 15 章 贪心
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15.1 贪心算法
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15.2 分数背包问题
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15.3 最大容量问题
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15.4 最大切分乘积问题
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15.5 小结
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第 16 章 附录
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第 16 章 附录
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16.1 编程环境安装
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16.2 一起参与创作
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1. 逐行放置策略
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2. 列与对角线剪枝
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3. 代码实现
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< h1 id = "134-n" > 13.4 N 皇后问题< a class = "headerlink" href = "#134-n" title = "Permanent link" > ¶ < / a > < / h1 >
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< div class = "admonition question" >
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< p class = "admonition-title" > Question< / p >
< p > 根据国际象棋的规则，皇后可以攻击与之处在同一行或同一列或同一斜线上的棋子。给定 < span class = "arithmatex" > \(n\)< / span > 个皇后和一个 < span class = "arithmatex" > \(n \times n\)< / span > 大小的棋盘，寻找使得所有皇后之间无法相互攻击的摆放方案。< / p >
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< / div >
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< p > 如图 13-15 所示，当 < span class = "arithmatex" > \(n = 4\)< / span > 时，共可以找到两个解。从回溯算法的角度看，< span class = "arithmatex" > \(n \times n\)< / span > 大小的棋盘共有 < span class = "arithmatex" > \(n^2\)< / span > 个格子，给出了所有的选择 < code > choices< / code > 。在逐个放置皇后的过程中，棋盘状态在不断地变化，每个时刻的棋盘就是状态 < code > state< / code > 。< / p >
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< p > < a class = "glightbox" href = "../n_queens_problem.assets/solution_4_queens.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "4 皇后问题的解" src = "../n_queens_problem.assets/solution_4_queens.png" / > < / a > < / p >
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< p align = "center" > 图 13-15 4 皇后问题的解 < / p >
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< p > 图 13-16 展示了本题的三个约束条件：< strong > 多个皇后不能在同一行、同一列、同一对角线< / strong > 。值得注意的是，对角线分为主对角线 < code > \< / code > 和次对角线 < code > /< / code > 两种。< / p >
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< p > < a class = "glightbox" href = "../n_queens_problem.assets/n_queens_constraints.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "n 皇后问题的约束条件" src = "../n_queens_problem.assets/n_queens_constraints.png" / > < / a > < / p >
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< p align = "center" > 图 13-16 n 皇后问题的约束条件 < / p >
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< h3 id = "1" > 1. 逐行放置策略< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 皇后的数量和棋盘的行数都为 < span class = "arithmatex" > \(n\)< / span > ，因此我们容易得到一个推论：< strong > 棋盘每行都允许且只允许放置一个皇后< / strong > 。< / p >
< p > 也就是说，我们可以采取逐行放置策略：从第一行开始，在每行放置一个皇后，直至最后一行结束。< / p >
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< p > 如图 13-17 所示，为 < span class = "arithmatex" > \(4\)< / span > 皇后问题的逐行放置过程。受画幅限制，图 13-17 仅展开了第一行的其中一个搜索分支，并且将不满足列约束和对角线约束的方案都进行了剪枝。< / p >
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< p > < a class = "glightbox" href = "../n_queens_problem.assets/n_queens_placing.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "逐行放置策略" src = "../n_queens_problem.assets/n_queens_placing.png" / > < / a > < / p >
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< p align = "center" > 图 13-17 逐行放置策略 < / p >
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< p > 本质上看，< strong > 逐行放置策略起到了剪枝的作用< / strong > ，它避免了同一行出现多个皇后的所有搜索分支。< / p >
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< h3 id = "2" > 2. 列与对角线剪枝< a class = "headerlink" href = "#2" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 为了满足列约束，我们可以利用一个长度为 < span class = "arithmatex" > \(n\)< / span > 的布尔型数组 < code > cols< / code > 记录每一列是否有皇后。在每次决定放置前，我们通过 < code > cols< / code > 将已有皇后的列进行剪枝，并在回溯中动态更新 < code > cols< / code > 的状态。< / p >
< p > 那么，如何处理对角线约束呢？设棋盘中某个格子的行列索引为 < span class = "arithmatex" > \((row, col)\)< / span > ，选定矩阵中的某条主对角线，我们发现该对角线上所有格子的行索引减列索引都相等，< strong > 即对角线上所有格子的 < span class = "arithmatex" > \(row - col\)< / span > 为恒定值< / strong > 。< / p >
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< p > 也就是说，如果两个格子满足 < span class = "arithmatex" > \(row_1 - col_1 = row_2 - col_2\)< / span > ，则它们一定处在同一条主对角线上。利用该规律，我们可以借助图 13-18 所示的数组 < code > diag1< / code > ，记录每条主对角线上是否有皇后。< / p >
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< p > 同理，< strong > 次对角线上的所有格子的 < span class = "arithmatex" > \(row + col\)< / span > 是恒定值< / strong > 。我们同样也可以借助数组 < code > diag2< / code > 来处理次对角线约束。< / p >
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< p > < a class = "glightbox" href = "../n_queens_problem.assets/n_queens_cols_diagonals.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "处理列约束和对角线约束" src = "../n_queens_problem.assets/n_queens_cols_diagonals.png" / > < / a > < / p >
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< p align = "center" > 图 13-18 处理列约束和对角线约束 < / p >
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< h3 id = "3" > 3. 代码实现< a class = "headerlink" href = "#3" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 请注意，< span class = "arithmatex" > \(n\)< / span > 维方阵中 < span class = "arithmatex" > \(row - col\)< / span > 的范围是 < span class = "arithmatex" > \([-n + 1, n - 1]\)< / span > ， < span class = "arithmatex" > \(row + col\)< / span > 的范围是 < span class = "arithmatex" > \([0, 2n - 2]\)< / span > ，所以主对角线和次对角线的数量都为 < span class = "arithmatex" > \(2n - 1\)< / span > ，即数组 < code > diag1< / code > 和 < code > diag2< / code > 的长度都为 < span class = "arithmatex" > \(2n - 1\)< / span > 。< / p >
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< div class = "highlight" > < span class = "filename" > n_queens.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "n" > row< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > str< / span > < span class = "p" > ]],< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > str< / span > < span class = "p" > ]]],< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "n" > cols< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > bool< / span > < span class = "p" > ],< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "n" > diags1< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > bool< / span > < span class = "p" > ],< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "n" > diags2< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > bool< / span > < span class = "p" > ],< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "p" > ):< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法： " " " < / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "c1" > # 当放置完所有行时，记录解< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "k" > if< / span > < span class = "n" > row< / span > < span class = "o" > ==< / span > < span class = "n" > n< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > ([< / span > < span class = "nb" > list< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > )< / span > < span class = "k" > for< / span > < span class = "n" > row< / span > < span class = "ow" > in< / span > < span class = "n" > state< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "c1" > # 遍历所有列< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "k" > for< / span > < span class = "n" > col< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "c1" > # 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "n" > diag1< / span > < span class = "o" > =< / span > < span class = "n" > row< / span > < span class = "o" > -< / span > < span class = "n" > col< / span > < span class = "o" > +< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "n" > diag2< / span > < span class = "o" > =< / span > < span class = "n" > row< / span > < span class = "o" > +< / span > < span class = "n" > col< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "c1" > # 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "k" > if< / span > < span class = "ow" > not< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "ow" > and< / span > < span class = "ow" > not< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "ow" > and< / span > < span class = "ow" > not< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "c1" > # 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "s2" > " Q" < / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "c1" > # 放置下一行< / span >
< a id = "__codelineno-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-27" name = "__codelineno-0-27" href = "#__codelineno-0-27" > < / a > < span class = "c1" > # 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-0-28" name = "__codelineno-0-28" href = "#__codelineno-0-28" > < / a > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "s2" > " #" < / span >
< a id = "__codelineno-0-29" name = "__codelineno-0-29" href = "#__codelineno-0-29" > < / a > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > False< / span >
< a id = "__codelineno-0-30" name = "__codelineno-0-30" href = "#__codelineno-0-30" > < / a >
< a id = "__codelineno-0-31" name = "__codelineno-0-31" href = "#__codelineno-0-31" > < / a > < span class = "k" > def< / span > < span class = "nf" > n_queens< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > str< / span > < span class = "p" > ]]]:< / span >
< a id = "__codelineno-0-32" name = "__codelineno-0-32" href = "#__codelineno-0-32" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 求解 N 皇后" " " < / span >
< a id = "__codelineno-0-33" name = "__codelineno-0-33" href = "#__codelineno-0-33" > < / a > < span class = "c1" > # 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-0-34" name = "__codelineno-0-34" href = "#__codelineno-0-34" > < / a > < span class = "n" > state< / span > < span class = "o" > =< / span > < span class = "p" > [[< / span > < span class = "s2" > " #" < / span > < span class = "k" > for< / span > < span class = "n" > _< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > )]< / span > < span class = "k" > for< / span > < span class = "n" > _< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > )]< / span >
< a id = "__codelineno-0-35" name = "__codelineno-0-35" href = "#__codelineno-0-35" > < / a > < span class = "n" > cols< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "kc" > False< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "c1" > # 记录列是否有皇后< / span >
< a id = "__codelineno-0-36" name = "__codelineno-0-36" href = "#__codelineno-0-36" > < / a > < span class = "n" > diags1< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "kc" > False< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "c1" > # 记录主对角线是否有皇后< / span >
< a id = "__codelineno-0-37" name = "__codelineno-0-37" href = "#__codelineno-0-37" > < / a > < span class = "n" > diags2< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "kc" > False< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "c1" > # 记录副对角线是否有皇后< / span >
< a id = "__codelineno-0-38" name = "__codelineno-0-38" href = "#__codelineno-0-38" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-0-39" name = "__codelineno-0-39" href = "#__codelineno-0-39" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-40" name = "__codelineno-0-40" href = "#__codelineno-0-40" > < / a >
< a id = "__codelineno-0-41" name = "__codelineno-0-41" href = "#__codelineno-0-41" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > nQueens< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-30" name = "__codelineno-1-30" href = "#__codelineno-1-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-1-31" name = "__codelineno-1-31" href = "#__codelineno-1-31" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > ));< / span >
< a id = "__codelineno-1-32" name = "__codelineno-1-32" href = "#__codelineno-1-32" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-1-33" name = "__codelineno-1-33" href = "#__codelineno-1-33" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > (< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-1-34" name = "__codelineno-1-34" href = "#__codelineno-1-34" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > (< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-1-35" name = "__codelineno-1-35" href = "#__codelineno-1-35" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-36" name = "__codelineno-1-36" href = "#__codelineno-1-36" > < / a >
< a id = "__codelineno-1-37" name = "__codelineno-1-37" href = "#__codelineno-1-37" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-38" name = "__codelineno-1-38" href = "#__codelineno-1-38" > < / a >
< a id = "__codelineno-1-39" name = "__codelineno-1-39" href = "#__codelineno-1-39" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-40" name = "__codelineno-1-40" href = "#__codelineno-1-40" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > copyState< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > sRow< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "w" > < / span > < span class = "n" > copyState< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > (< / span > < span class = "n" > sRow< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > copyState< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > cols< / span > < span class = "o" > [< / span > < span class = "n" > col< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags1< / span > < span class = "o" > [< / span > < span class = "n" > diag1< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags2< / span > < span class = "o" > [< / span > < span class = "n" > diag2< / span > < span class = "o" > ]< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > ).< / span > < span class = "na" > set< / span > < span class = "p" > (< / span > < span class = "n" > col< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "o" > [< / span > < span class = "n" > col< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "o" > [< / span > < span class = "n" > diag1< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "o" > [< / span > < span class = "n" > diag2< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > ).< / span > < span class = "na" > set< / span > < span class = "p" > (< / span > < span class = "n" > col< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "o" > [< / span > < span class = "n" > col< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "o" > [< / span > < span class = "n" > diag1< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "o" > [< / span > < span class = "n" > diag2< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-30" name = "__codelineno-2-30" href = "#__codelineno-2-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-2-31" name = "__codelineno-2-31" href = "#__codelineno-2-31" > < / a >
< a id = "__codelineno-2-32" name = "__codelineno-2-32" href = "#__codelineno-2-32" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-2-33" name = "__codelineno-2-33" href = "#__codelineno-2-33" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "nf" > nQueens< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-34" name = "__codelineno-2-34" href = "#__codelineno-2-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-2-35" name = "__codelineno-2-35" href = "#__codelineno-2-35" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-2-36" name = "__codelineno-2-36" href = "#__codelineno-2-36" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-37" name = "__codelineno-2-37" href = "#__codelineno-2-37" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-2-38" name = "__codelineno-2-38" href = "#__codelineno-2-38" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-39" name = "__codelineno-2-39" href = "#__codelineno-2-39" > < / a > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "s" > " #" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-40" name = "__codelineno-2-40" href = "#__codelineno-2-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-41" name = "__codelineno-2-41" href = "#__codelineno-2-41" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-42" name = "__codelineno-2-42" href = "#__codelineno-2-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-43" name = "__codelineno-2-43" href = "#__codelineno-2-43" > < / a > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > [< / span > < span class = "n" > n< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-2-44" name = "__codelineno-2-44" href = "#__codelineno-2-44" > < / a > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > [< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-2-45" name = "__codelineno-2-45" href = "#__codelineno-2-45" > < / a > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > [< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-2-46" name = "__codelineno-2-46" href = "#__codelineno-2-46" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-2-47" name = "__codelineno-2-47" href = "#__codelineno-2-47" > < / a >
< a id = "__codelineno-2-48" name = "__codelineno-2-48" href = "#__codelineno-2-48" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-49" name = "__codelineno-2-49" href = "#__codelineno-2-49" > < / a >
< a id = "__codelineno-2-50" name = "__codelineno-2-50" href = "#__codelineno-2-50" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-51" name = "__codelineno-2-51" href = "#__codelineno-2-51" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > Backtrack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > copyState< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "k" > foreach< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > sRow< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "n" > copyState< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > sRow< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > copyState< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "n" > Backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a >
< a id = "__codelineno-3-32" name = "__codelineno-3-32" href = "#__codelineno-3-32" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-33" name = "__codelineno-3-33" href = "#__codelineno-3-33" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > NQueens< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-34" name = "__codelineno-3-34" href = "#__codelineno-3-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-35" name = "__codelineno-3-35" href = "#__codelineno-3-35" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-36" name = "__codelineno-3-36" href = "#__codelineno-3-36" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-37" name = "__codelineno-3-37" href = "#__codelineno-3-37" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-38" name = "__codelineno-3-38" href = "#__codelineno-3-38" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-39" name = "__codelineno-3-39" href = "#__codelineno-3-39" > < / a > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "s" > " #" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-40" name = "__codelineno-3-40" href = "#__codelineno-3-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-41" name = "__codelineno-3-41" href = "#__codelineno-3-41" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-42" name = "__codelineno-3-42" href = "#__codelineno-3-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-43" name = "__codelineno-3-43" href = "#__codelineno-3-43" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-3-44" name = "__codelineno-3-44" href = "#__codelineno-3-44" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > [< / span > < span class = "m" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-3-45" name = "__codelineno-3-45" href = "#__codelineno-3-45" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > [< / span > < span class = "m" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-46" name = "__codelineno-3-46" href = "#__codelineno-3-46" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-47" name = "__codelineno-3-47" href = "#__codelineno-3-47" > < / a >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-48" name = "__codelineno-3-48" href = "#__codelineno-3-48" > < / a > < span class = "w" > < / span > < span class = "n" > Backtrack< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-49" name = "__codelineno-3-49" href = "#__codelineno-3-49" > < / a >
< a id = "__codelineno-3-50" name = "__codelineno-3-50" href = "#__codelineno-3-50" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-51" name = "__codelineno-3-51" href = "#__codelineno-3-51" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "kt" > bool< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > ((< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "mi" > 0< / span > < span class = "p" > ]))< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "nb" > copy< / span > < span class = "p" > (< / span > < span class = "nx" > newState< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "nx" > diag1< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "nx" > diag2< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > col< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > !(< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "p" > !(< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "p" > !(< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span >
< a id = "__codelineno-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-30" name = "__codelineno-4-30" href = "#__codelineno-4-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-31" name = "__codelineno-4-31" href = "#__codelineno-4-31" > < / a >
< a id = "__codelineno-4-32" name = "__codelineno-4-32" href = "#__codelineno-4-32" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-4-33" name = "__codelineno-4-33" href = "#__codelineno-4-33" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "kt" > bool< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-34" name = "__codelineno-4-34" href = "#__codelineno-4-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-4-35" name = "__codelineno-4-35" href = "#__codelineno-4-35" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-36" name = "__codelineno-4-36" href = "#__codelineno-4-36" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-4-37" name = "__codelineno-4-37" href = "#__codelineno-4-37" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-38" name = "__codelineno-4-38" href = "#__codelineno-4-38" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > ((< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "mi" > 0< / span > < span class = "p" > ]))< / span >
< a id = "__codelineno-4-39" name = "__codelineno-4-39" href = "#__codelineno-4-39" > < / a > < span class = "w" > < / span > < span class = "nb" > copy< / span > < span class = "p" > (< / span > < span class = "nx" > newState< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-4-40" name = "__codelineno-4-40" href = "#__codelineno-4-40" > < / a >
< a id = "__codelineno-4-41" name = "__codelineno-4-41" href = "#__codelineno-4-41" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-42" name = "__codelineno-4-42" href = "#__codelineno-4-42" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-43" name = "__codelineno-4-43" href = "#__codelineno-4-43" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-44" name = "__codelineno-4-44" href = "#__codelineno-4-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-4-45" name = "__codelineno-4-45" href = "#__codelineno-4-45" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-46" name = "__codelineno-4-46" href = "#__codelineno-4-46" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-4-47" name = "__codelineno-4-47" href = "#__codelineno-4-47" > < / a > < span class = "w" > < / span > < span class = "nx" > diag1< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-4-48" name = "__codelineno-4-48" href = "#__codelineno-4-48" > < / a > < span class = "w" > < / span > < span class = "nx" > diag2< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > col< / span >
< a id = "__codelineno-4-49" name = "__codelineno-4-49" href = "#__codelineno-4-49" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-4-50" name = "__codelineno-4-50" href = "#__codelineno-4-50" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > !(< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "p" > !(< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "p" > !(< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-51" name = "__codelineno-4-51" href = "#__codelineno-4-51" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-4-52" name = "__codelineno-4-52" href = "#__codelineno-4-52" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span >
< a id = "__codelineno-4-53" name = "__codelineno-4-53" href = "#__codelineno-4-53" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span >
< a id = "__codelineno-4-54" name = "__codelineno-4-54" href = "#__codelineno-4-54" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-4-55" name = "__codelineno-4-55" href = "#__codelineno-4-55" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-56" name = "__codelineno-4-56" href = "#__codelineno-4-56" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-4-57" name = "__codelineno-4-57" href = "#__codelineno-4-57" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span >
< a id = "__codelineno-4-58" name = "__codelineno-4-58" href = "#__codelineno-4-58" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span >
< a id = "__codelineno-4-59" name = "__codelineno-4-59" href = "#__codelineno-4-59" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-60" name = "__codelineno-4-60" href = "#__codelineno-4-60" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-61" name = "__codelineno-4-61" href = "#__codelineno-4-61" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-62" name = "__codelineno-4-62" href = "#__codelineno-4-62" > < / a >
< a id = "__codelineno-4-63" name = "__codelineno-4-63" href = "#__codelineno-4-63" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > nQueens< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > [][][]< / span > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-64" name = "__codelineno-4-64" href = "#__codelineno-4-64" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-4-65" name = "__codelineno-4-65" href = "#__codelineno-4-65" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-66" name = "__codelineno-4-66" href = "#__codelineno-4-66" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-67" name = "__codelineno-4-67" href = "#__codelineno-4-67" > < / a > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-68" name = "__codelineno-4-68" href = "#__codelineno-4-68" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-69" name = "__codelineno-4-69" href = "#__codelineno-4-69" > < / a > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span >
< a id = "__codelineno-4-70" name = "__codelineno-4-70" href = "#__codelineno-4-70" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-71" name = "__codelineno-4-71" href = "#__codelineno-4-71" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span >
< a id = "__codelineno-4-72" name = "__codelineno-4-72" href = "#__codelineno-4-72" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-73" name = "__codelineno-4-73" href = "#__codelineno-4-73" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-4-74" name = "__codelineno-4-74" href = "#__codelineno-4-74" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > bool< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-75" name = "__codelineno-4-75" href = "#__codelineno-4-75" > < / a > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > bool< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-76" name = "__codelineno-4-76" href = "#__codelineno-4-76" > < / a > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > bool< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-77" name = "__codelineno-4-77" href = "#__codelineno-4-77" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([][][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-78" name = "__codelineno-4-78" href = "#__codelineno-4-78" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-79" name = "__codelineno-4-79" href = "#__codelineno-4-79" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-4-80" name = "__codelineno-4-80" href = "#__codelineno-4-80" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [[< / span > < span class = "nb" > String< / span > < span class = "p" > ]],< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [[[< / span > < span class = "nb" > String< / span > < span class = "p" > ]]],< / span > < span class = "n" > cols< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Bool< / span > < span class = "p" > ],< / span > < span class = "n" > diags1< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Bool< / span > < span class = "p" > ],< / span > < span class = "n" > diags2< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Bool< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "k" > if< / span > < span class = "n" > row< / span > < span class = "p" > ==< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "k" > for< / span > < span class = "n" > col< / span > < span class = "k" > in< / span > < span class = "mi" > 0< / span > < span class = "p" > ..< / span > < span class = "o" > < < / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "kd" > let< / span > < span class = "nv" > diag1< / span > < span class = "p" > =< / span > < span class = "n" > row< / span > < span class = "o" > -< / span > < span class = "n" > col< / span > < span class = "o" > +< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "kd" > let< / span > < span class = "nv" > diag2< / span > < span class = "p" > =< / span > < span class = "n" > row< / span > < span class = "o" > +< / span > < span class = "n" > col< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "k" > if< / span > < span class = "o" > !< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > & & < / span > < span class = "o" > !< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "o" > & & < / span > < span class = "o" > !< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "s" > " Q" < / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > :< / span > < span class = "n" > row< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > cols< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "n" > diags1< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "n" > diags2< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "s" > " #" < / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > false< / span >
< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / a > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > false< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > false< / span >
< a id = "__codelineno-5-27" name = "__codelineno-5-27" href = "#__codelineno-5-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-28" name = "__codelineno-5-28" href = "#__codelineno-5-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-29" name = "__codelineno-5-29" href = "#__codelineno-5-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-30" name = "__codelineno-5-30" href = "#__codelineno-5-30" > < / a >
< a id = "__codelineno-5-31" name = "__codelineno-5-31" href = "#__codelineno-5-31" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-5-32" name = "__codelineno-5-32" href = "#__codelineno-5-32" > < / a > < span class = "kd" > func< / span > < span class = "nf" > nQueens< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "p" > [[[< / span > < span class = "nb" > String< / span > < span class = "p" > ]]]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-33" name = "__codelineno-5-33" href = "#__codelineno-5-33" > < / a > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-5-34" name = "__codelineno-5-34" href = "#__codelineno-5-34" > < / a > < span class = "kd" > var< / span > < span class = "nv" > state< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "s" > " #" < / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ),< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-35" name = "__codelineno-5-35" href = "#__codelineno-5-35" > < / a > < span class = "kd" > var< / span > < span class = "nv" > cols< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-5-36" name = "__codelineno-5-36" href = "#__codelineno-5-36" > < / a > < span class = "kd" > var< / span > < span class = "nv" > diags1< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-5-37" name = "__codelineno-5-37" href = "#__codelineno-5-37" > < / a > < span class = "kd" > var< / span > < span class = "nv" > diags2< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-5-38" name = "__codelineno-5-38" href = "#__codelineno-5-38" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > :< / span > < span class = "p" > [[[< / span > < span class = "nb" > String< / span > < span class = "p" > ]]]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-5-39" name = "__codelineno-5-39" href = "#__codelineno-5-39" > < / a >
< a id = "__codelineno-5-40" name = "__codelineno-5-40" href = "#__codelineno-5-40" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > cols< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "n" > diags1< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "n" > diags2< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-41" name = "__codelineno-5-41" href = "#__codelineno-5-41" > < / a >
< a id = "__codelineno-5-42" name = "__codelineno-5-42" href = "#__codelineno-5-42" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-5-43" name = "__codelineno-5-43" href = "#__codelineno-5-43" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > map< / span > < span class = "p" > ((< / span > < span class = "nx" > row< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "p" > .< / span > < span class = "nx" > slice< / span > < span class = "p" > ()));< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-10" name = "__codelineno-6-10" href = "#__codelineno-6-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-6-11" name = "__codelineno-6-11" href = "#__codelineno-6-11" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-12" name = "__codelineno-6-12" href = "#__codelineno-6-12" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-13" name = "__codelineno-6-13" href = "#__codelineno-6-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-6-14" name = "__codelineno-6-14" href = "#__codelineno-6-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-15" name = "__codelineno-6-15" href = "#__codelineno-6-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-6-16" name = "__codelineno-6-16" href = "#__codelineno-6-16" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' Q' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-17" name = "__codelineno-6-17" href = "#__codelineno-6-17" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-18" name = "__codelineno-6-18" href = "#__codelineno-6-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-6-19" name = "__codelineno-6-19" href = "#__codelineno-6-19" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-20" name = "__codelineno-6-20" href = "#__codelineno-6-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-6-21" name = "__codelineno-6-21" href = "#__codelineno-6-21" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' #' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-22" name = "__codelineno-6-22" href = "#__codelineno-6-22" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-23" name = "__codelineno-6-23" href = "#__codelineno-6-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-24" name = "__codelineno-6-24" href = "#__codelineno-6-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-25" name = "__codelineno-6-25" href = "#__codelineno-6-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-6-26" name = "__codelineno-6-26" href = "#__codelineno-6-26" > < / a >
< a id = "__codelineno-6-27" name = "__codelineno-6-27" href = "#__codelineno-6-27" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-6-28" name = "__codelineno-6-28" href = "#__codelineno-6-28" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > nQueens< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-29" name = "__codelineno-6-29" href = "#__codelineno-6-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-6-30" name = "__codelineno-6-30" href = "#__codelineno-6-30" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > .< / span > < span class = "kr" > from< / span > < span class = "p" > ({< / span > < span class = "w" > < / span > < span class = "nx" > length< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > },< / span > < span class = "w" > < / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "s1" > ' #' < / span > < span class = "p" > ));< / span >
< a id = "__codelineno-6-31" name = "__codelineno-6-31" href = "#__codelineno-6-31" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-6-32" name = "__codelineno-6-32" href = "#__codelineno-6-32" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-6-33" name = "__codelineno-6-33" href = "#__codelineno-6-33" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-6-34" name = "__codelineno-6-34" href = "#__codelineno-6-34" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-6-35" name = "__codelineno-6-35" href = "#__codelineno-6-35" > < / a >
< a id = "__codelineno-6-36" name = "__codelineno-6-36" href = "#__codelineno-6-36" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-37" name = "__codelineno-6-37" href = "#__codelineno-6-37" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-38" name = "__codelineno-6-38" href = "#__codelineno-6-38" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > [][],< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > [][][],< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "p" > []< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > map< / span > < span class = "p" > ((< / span > < span class = "nx" > row< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "p" > .< / span > < span class = "nx" > slice< / span > < span class = "p" > ()));< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' Q' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-28" name = "__codelineno-7-28" href = "#__codelineno-7-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-7-29" name = "__codelineno-7-29" href = "#__codelineno-7-29" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' #' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-30" name = "__codelineno-7-30" href = "#__codelineno-7-30" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-31" name = "__codelineno-7-31" href = "#__codelineno-7-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-32" name = "__codelineno-7-32" href = "#__codelineno-7-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-33" name = "__codelineno-7-33" href = "#__codelineno-7-33" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-34" name = "__codelineno-7-34" href = "#__codelineno-7-34" > < / a >
< a id = "__codelineno-7-35" name = "__codelineno-7-35" href = "#__codelineno-7-35" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-7-36" name = "__codelineno-7-36" href = "#__codelineno-7-36" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > nQueens< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > [][][]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-37" name = "__codelineno-7-37" href = "#__codelineno-7-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-7-38" name = "__codelineno-7-38" href = "#__codelineno-7-38" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > .< / span > < span class = "kr" > from< / span > < span class = "p" > ({< / span > < span class = "w" > < / span > < span class = "nx" > length< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > n< / span > < span class = "w" > < / span > < span class = "p" > },< / span > < span class = "w" > < / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "s1" > ' #' < / span > < span class = "p" > ));< / span >
< a id = "__codelineno-7-39" name = "__codelineno-7-39" href = "#__codelineno-7-39" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-7-40" name = "__codelineno-7-40" href = "#__codelineno-7-40" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-7-41" name = "__codelineno-7-41" href = "#__codelineno-7-41" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-7-42" name = "__codelineno-7-42" href = "#__codelineno-7-42" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > [][][]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-7-43" name = "__codelineno-7-43" href = "#__codelineno-7-43" > < / a >
< a id = "__codelineno-7-44" name = "__codelineno-7-44" href = "#__codelineno-7-44" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-45" name = "__codelineno-7-45" href = "#__codelineno-7-45" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-46" name = "__codelineno-7-46" href = "#__codelineno-7-46" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > copyState< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > String< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > sRow< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "w" > < / span > < span class = "n" > copyState< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > from< / span > < span class = "p" > (< / span > < span class = "n" > sRow< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > copyState< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-8-28" name = "__codelineno-8-28" href = "#__codelineno-8-28" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s2" > " Q" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-29" name = "__codelineno-8-29" href = "#__codelineno-8-29" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-30" name = "__codelineno-8-30" href = "#__codelineno-8-30" > < / a > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-31" name = "__codelineno-8-31" href = "#__codelineno-8-31" > < / a > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-32" name = "__codelineno-8-32" href = "#__codelineno-8-32" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-8-33" name = "__codelineno-8-33" href = "#__codelineno-8-33" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-34" name = "__codelineno-8-34" href = "#__codelineno-8-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-8-35" name = "__codelineno-8-35" href = "#__codelineno-8-35" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s2" > " #" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-36" name = "__codelineno-8-36" href = "#__codelineno-8-36" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-37" name = "__codelineno-8-37" href = "#__codelineno-8-37" > < / a > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-38" name = "__codelineno-8-38" href = "#__codelineno-8-38" > < / a > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-39" name = "__codelineno-8-39" href = "#__codelineno-8-39" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-40" name = "__codelineno-8-40" href = "#__codelineno-8-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-41" name = "__codelineno-8-41" href = "#__codelineno-8-41" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-42" name = "__codelineno-8-42" href = "#__codelineno-8-42" > < / a >
< a id = "__codelineno-8-43" name = "__codelineno-8-43" href = "#__codelineno-8-43" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-8-44" name = "__codelineno-8-44" href = "#__codelineno-8-44" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > nQueens< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-45" name = "__codelineno-8-45" href = "#__codelineno-8-45" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-8-46" name = "__codelineno-8-46" href = "#__codelineno-8-46" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > generate< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > index< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > => < / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > filled< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s2" > " #" < / span > < span class = "p" > ));< / span >
< a id = "__codelineno-8-47" name = "__codelineno-8-47" href = "#__codelineno-8-47" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > filled< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-8-48" name = "__codelineno-8-48" href = "#__codelineno-8-48" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > filled< / span > < span class = "p" > (< / span > < span class = "m" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-8-49" name = "__codelineno-8-49" href = "#__codelineno-8-49" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > filled< / span > < span class = "p" > (< / span > < span class = "m" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-8-50" name = "__codelineno-8-50" href = "#__codelineno-8-50" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-8-51" name = "__codelineno-8-51" href = "#__codelineno-8-51" > < / a >
< a id = "__codelineno-8-52" name = "__codelineno-8-52" href = "#__codelineno-8-52" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-53" name = "__codelineno-8-53" href = "#__codelineno-8-53" > < / a >
< a id = "__codelineno-8-54" name = "__codelineno-8-54" href = "#__codelineno-8-54" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-55" name = "__codelineno-8-55" href = "#__codelineno-8-55" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > : < span class = "kt" > usize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > : < span class = "kt" > usize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > String< / span > < span class = "o" > > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > String< / span > < span class = "o" > > > > < / span > < span class = "p" > ,< / span >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "kt" > bool< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "kt" > bool< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "kt" > bool< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > copy_state< / span > : < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > s_row< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > clone< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "w" > < / span > < span class = "n" > copy_state< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > s_row< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-10" name = "__codelineno-9-10" href = "#__codelineno-9-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > copy_state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-11" name = "__codelineno-9-11" href = "#__codelineno-9-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-12" name = "__codelineno-9-12" href = "#__codelineno-9-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-13" name = "__codelineno-9-13" href = "#__codelineno-9-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-9-14" name = "__codelineno-9-14" href = "#__codelineno-9-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "o" > ..< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-15" name = "__codelineno-9-15" href = "#__codelineno-9-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-9-16" name = "__codelineno-9-16" href = "#__codelineno-9-16" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-17" name = "__codelineno-9-17" href = "#__codelineno-9-17" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-18" name = "__codelineno-9-18" href = "#__codelineno-9-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-9-19" name = "__codelineno-9-19" href = "#__codelineno-9-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-20" name = "__codelineno-9-20" href = "#__codelineno-9-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-9-21" name = "__codelineno-9-21" href = "#__codelineno-9-21" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > get_mut< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > ).< / span > < span class = "n" > unwrap< / span > < span class = "p" > ()[< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span > < span class = "p" > .< / span > < span class = "n" > into< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-22" name = "__codelineno-9-22" href = "#__codelineno-9-22" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-23" name = "__codelineno-9-23" href = "#__codelineno-9-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-9-24" name = "__codelineno-9-24" href = "#__codelineno-9-24" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-25" name = "__codelineno-9-25" href = "#__codelineno-9-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-9-26" name = "__codelineno-9-26" href = "#__codelineno-9-26" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > get_mut< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > ).< / span > < span class = "n" > unwrap< / span > < span class = "p" > ()[< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > .< / span > < span class = "n" > into< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-27" name = "__codelineno-9-27" href = "#__codelineno-9-27" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-28" name = "__codelineno-9-28" href = "#__codelineno-9-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-29" name = "__codelineno-9-29" href = "#__codelineno-9-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-30" name = "__codelineno-9-30" href = "#__codelineno-9-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-9-31" name = "__codelineno-9-31" href = "#__codelineno-9-31" > < / a >
< a id = "__codelineno-9-32" name = "__codelineno-9-32" href = "#__codelineno-9-32" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-9-33" name = "__codelineno-9-33" href = "#__codelineno-9-33" > < / a > < span class = "k" > fn< / span > < span class = "nf" > n_queens< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > usize< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-34" name = "__codelineno-9-34" href = "#__codelineno-9-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-9-35" name = "__codelineno-9-35" href = "#__codelineno-9-35" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > state< / span > : < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-36" name = "__codelineno-9-36" href = "#__codelineno-9-36" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "o" > ..< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-37" name = "__codelineno-9-37" href = "#__codelineno-9-37" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > row< / span > : < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > String< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-38" name = "__codelineno-9-38" href = "#__codelineno-9-38" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "o" > ..< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-39" name = "__codelineno-9-39" href = "#__codelineno-9-39" > < / a > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "s" > " #" < / span > < span class = "p" > .< / span > < span class = "n" > into< / span > < span class = "p" > ());< / span >
< a id = "__codelineno-9-40" name = "__codelineno-9-40" href = "#__codelineno-9-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-41" name = "__codelineno-9-41" href = "#__codelineno-9-41" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-42" name = "__codelineno-9-42" href = "#__codelineno-9-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-43" name = "__codelineno-9-43" href = "#__codelineno-9-43" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "fm" > vec!< / span > < span class = "p" > [< / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-9-44" name = "__codelineno-9-44" href = "#__codelineno-9-44" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "fm" > vec!< / span > < span class = "p" > [< / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-9-45" name = "__codelineno-9-45" href = "#__codelineno-9-45" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "fm" > vec!< / span > < span class = "p" > [< / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-9-46" name = "__codelineno-9-46" href = "#__codelineno-9-46" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > : < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-47" name = "__codelineno-9-47" href = "#__codelineno-9-47" > < / a >
< a id = "__codelineno-9-48" name = "__codelineno-9-48" href = "#__codelineno-9-48" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-49" name = "__codelineno-9-49" href = "#__codelineno-9-49" > < / a >
< a id = "__codelineno-9-50" name = "__codelineno-9-50" href = "#__codelineno-9-50" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-9-51" name = "__codelineno-9-51" href = "#__codelineno-9-51" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
2023-06-02 02:38:32 +08:00
< div class = "tabbed-block" >
2023-10-18 02:17:09 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > MAX_N< / span > < span class = "p" > ][< / span > < span class = "n" > MAX_N< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > ***< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > MAX_N< / span > < span class = "p" > ],< / span >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > MAX_N< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > MAX_N< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "p" > )< / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "o" > ++< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > ][< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )< / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "w" > < / span > < span class = "n" > strcpy< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > ][< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > )< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-13" name = "__codelineno-10-13" href = "#__codelineno-10-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-14" name = "__codelineno-10-14" href = "#__codelineno-10-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-10-15" name = "__codelineno-10-15" href = "#__codelineno-10-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-16" name = "__codelineno-10-16" href = "#__codelineno-10-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-10-17" name = "__codelineno-10-17" href = "#__codelineno-10-17" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-18" name = "__codelineno-10-18" href = "#__codelineno-10-18" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-19" name = "__codelineno-10-19" href = "#__codelineno-10-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后< / span >
< a id = "__codelineno-10-20" name = "__codelineno-10-20" href = "#__codelineno-10-20" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-21" name = "__codelineno-10-21" href = "#__codelineno-10-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-10-22" name = "__codelineno-10-22" href = "#__codelineno-10-22" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "sc" > ' Q' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-23" name = "__codelineno-10-23" href = "#__codelineno-10-23" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-24" name = "__codelineno-10-24" href = "#__codelineno-10-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-10-25" name = "__codelineno-10-25" href = "#__codelineno-10-25" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > resSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-26" name = "__codelineno-10-26" href = "#__codelineno-10-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-10-27" name = "__codelineno-10-27" href = "#__codelineno-10-27" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "sc" > ' #' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-28" name = "__codelineno-10-28" href = "#__codelineno-10-28" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-29" name = "__codelineno-10-29" href = "#__codelineno-10-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-30" name = "__codelineno-10-30" href = "#__codelineno-10-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-31" name = "__codelineno-10-31" href = "#__codelineno-10-31" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-32" name = "__codelineno-10-32" href = "#__codelineno-10-32" > < / a >
< a id = "__codelineno-10-33" name = "__codelineno-10-33" href = "#__codelineno-10-33" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-10-34" name = "__codelineno-10-34" href = "#__codelineno-10-34" > < / a > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > ***< / span > < span class = "nf" > nQueens< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > returnSize< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-35" name = "__codelineno-10-35" href = "#__codelineno-10-35" > < / a > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > MAX_N< / span > < span class = "p" > ][< / span > < span class = "n" > MAX_N< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-10-36" name = "__codelineno-10-36" href = "#__codelineno-10-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-10-37" name = "__codelineno-10-37" href = "#__codelineno-10-37" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "o" > ++< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-38" name = "__codelineno-10-38" href = "#__codelineno-10-38" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "o" > ++< / span > < span class = "n" > j< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-39" name = "__codelineno-10-39" href = "#__codelineno-10-39" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "sc" > ' #' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-40" name = "__codelineno-10-40" href = "#__codelineno-10-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-41" name = "__codelineno-10-41" href = "#__codelineno-10-41" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > n< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "sc" > ' \0' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-42" name = "__codelineno-10-42" href = "#__codelineno-10-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-43" name = "__codelineno-10-43" href = "#__codelineno-10-43" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > MAX_N< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "nb" > false< / span > < span class = "p" > };< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-10-44" name = "__codelineno-10-44" href = "#__codelineno-10-44" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > MAX_N< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "nb" > false< / span > < span class = "p" > };< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-10-45" name = "__codelineno-10-45" href = "#__codelineno-10-45" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > MAX_N< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "nb" > false< / span > < span class = "p" > };< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-10-46" name = "__codelineno-10-46" href = "#__codelineno-10-46" > < / a >
< a id = "__codelineno-10-47" name = "__codelineno-10-47" href = "#__codelineno-10-47" > < / a > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > ***< / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > ***< / span > < span class = "p" > )< / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > MAX_RES< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-48" name = "__codelineno-10-48" href = "#__codelineno-10-48" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > returnSize< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-49" name = "__codelineno-10-49" href = "#__codelineno-10-49" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > returnSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-50" name = "__codelineno-10-50" href = "#__codelineno-10-50" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-51" name = "__codelineno-10-51" href = "#__codelineno-10-51" > < / a > < span class = "p" > }< / span >
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< / div >
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< div class = "highlight" > < span class = "filename" > n_queens.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > backtrack< / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > nQueens< / span > < span class = "p" > }< / span >
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< / div >
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< p > 逐行放置 < span class = "arithmatex" > \(n\)< / span > 次，考虑列约束，则从第一行到最后一行分别有 < span class = "arithmatex" > \(n\)< / span > 、< span class = "arithmatex" > \(n-1\)< / span > 、< span class = "arithmatex" > \(\dots\)< / span > 、< span class = "arithmatex" > \(2\)< / span > 、< span class = "arithmatex" > \(1\)< / span > 个选择，< strong > 因此时间复杂度为 < span class = "arithmatex" > \(O(n!)\)< / span > < / strong > 。实际上，根据对角线约束的剪枝也能够大幅地缩小搜索空间，因而搜索效率往往优于以上时间复杂度。< / p >
< p > 数组 < code > state< / code > 使用 < span class = "arithmatex" > \(O(n^2)\)< / span > 空间，数组 < code > cols< / code > 、< code > diags1< / code > 和 < code > diags2< / code > 皆使用 < span class = "arithmatex" > \(O(n)\)< / span > 空间。最大递归深度为 < span class = "arithmatex" > \(n\)< / span > ，使用 < span class = "arithmatex" > \(O(n)\)< / span > 栈帧空间。因此，< strong > 空间复杂度为 < span class = "arithmatex" > \(O(n^2)\)< / span > < / strong > 。< / p >
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< script src = "../../javascripts/mathjax.js" > < / script >
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< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
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< script src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
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< script > document $ . subscribe ( ( ) => { const lightbox = GLightbox ( { "touchNavigation" : true , "loop" : false , "zoomable" : true , "draggable" : false , "openEffect" : "zoom" , "closeEffect" : "zoom" , "slideEffect" : "none" } ) ; } ) < / script > < / body >
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< / html >
